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Job Shop Scheduling using Ant Colony Optimization

Abstract

The classical Job shop Scheduling Problem (JSSP) considers the problem of efficiently

scheduling a finite number of jobs to a finite number of machines for processing. Each

job consists of a sequence of operations which have to be processed using a specified

machine for a specified amount of time, without any interruption. The operations

belonging to the same job have a technological sequence and none of them should begin

processing before the preceding operation has finished its execution. The challenge is tofind a feasible schedule consisting of the assignment of operations on machines without

violating these constraints. Also, the solution must specify the optimum makespan for the

schedule. The makespan is defined as the maximum completion time of all the jobs

considered. To optimize the makespan, it is necessary to make sure that the idleness of

machines is minimized. Thus, JSSP is a NP-hard combinatorial optimization problem and

obtaining the actual solution for JSSP is computationally difficult.

Ant Colony Optimization (ACO) technique is inspired by foraging behaviour of ants in

nature. ACO tries to mimic the observed behaviour of ants while they conduct a search

for an efficient path to follow to carry their food back to the nest. In a similar fashion, in

ACO, the concept of an ant is considered. Each ant constructively builds a solution to the

problem at hand by making decisions using path probabilities at each decision point.

ACO has been used extensively to present effective solutions to many combinatorial

optimization problems like Travelling Salesman problem and Vehicle routing problem. In

this project, we apply and analyze the effectiveness of Ant colony optimization for Job

shop Scheduling Problem (JSSP).

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Methodology

To apply ACO for JSSP, it is necessary to plot the given JSSP problem in the form

of a graph where nodes represent the operations and the execution time

represents the edge weights. Two dummy nodes, Start and Destination are addedto the graph. Once the graph is plotted, the problem converts to Travelling

Salesman Problem and we have to find the optimal path from Start to Destination.

Ants are placed at the Start node, and are made to traverse the whole graph and

reach the Destination node. While traversing, each ant is allowed to visit a node

only once. Whenever the ant wants to move to next node, it calculates the

probability of other nodes.

Unlike TSP, in JSSP, probability for each remaining node is not calculated since

technological sequence needs to be satisfied. So, to satisfy the constraint, the

visiting set Sk is maintained. Sk is initialized to starting nodes of each operation,where n is number of jobs.

Sk= {ui1| i [1, n]}

The ant is allowed to choose the next node only from those in Sk. After an ant

chooses the nodes in Skto visit, the chosen node is removed and its successor node

in the given task is added in its place. The procedure is continued until all nodes

are visited and the ant reaches the destination node. After the ant reaches the

destination node, its path cost is calculated.

References

[1] Anitha, J., and M. Karpagam. "Ant colony optimization using pheromone updating

strategy to solve job shop scheduling." In Intelligent Systems and Control (ISCO), 2013

7th International Conference on, pp. 367-372. IEEE, 2013.

[2] Chaukwale, Rajesh, and S. Sowmya Kamath. "A modified Ant Colony optimizationalgorithm with load balancing for job shop scheduling." In Advanced Computing

Technologies (ICACT), 2013 15th International Conference on, pp. 1-5. IEEE, 2013.